Scales are made with different divisions for different purposes. For machine, structural and architectural drawing the architects' scale of proportional feet and inches is used.

The Scale of the Architects

Scales are made with different divisions for different purposes. For machine, structural and architectural…

Illustration of equal circles to show that two central angles have the same ratio as their intercepted arcs.

Equal Circles With Intercepted Arcs

Illustration of equal circles to show that two central angles have the same ratio as their intercepted…

Illustration of 2 narrow right circular cylinders with equal heights (thickness) and different diameters. Both cylinders (discs) are resting on a side/edge.

2 Narrow Cylinders on Their Sides

Illustration of 2 narrow right circular cylinders with equal heights (thickness) and different diameters.…

Illustration of 2 right circular cylinders in which one cylinder is twice the height of the other.

2 Right Circular Cylinders

Illustration of 2 right circular cylinders in which one cylinder is twice the height of the other.

Illustration of 2 right circular cylinders in which one cylinder is twice the height and twice the diameter of the other.

2 Right Circular Cylinders

Illustration of 2 right circular cylinders in which one cylinder is twice the height and twice the diameter…

2 circles that are similar figures

Similar Figures

2 circles that are similar figures

2 squares that are similar figures

Similar Figures

2 squares that are similar figures

2 rectangles that are similar figures

Similar Figures

2 rectangles that are similar figures

2 pentagons that are similar figures

Similar Figures

2 pentagons that are similar figures

Illustration of an extension ladder. If ladder is leaned against a building, it will form a right triangle with the ground.

Extension Ladder

Illustration of an extension ladder. If ladder is leaned against a building, it will form a right triangle…

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned toward a building, it will form the hypotenuse of a right triangle.

Leaning Ladder

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned…

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned toward a building, it will form the hypotenuse of a right triangle.

Leaning Ladder

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned…

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned toward a building, it will form the hypotenuse of a right triangle.

Leaning Ladder

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned…

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned toward a building, it will form the hypotenuse of a right triangle.

Leaning Ladder

Illustration of a ladder that is not perpendicular to the ground. If it is set on the ground and leaned…

Illustration of a ladder leaning against the side of a building (wall) to form a right triangle .

Ladder Leaning Against a Building

Illustration of a ladder leaning against the side of a building (wall) to form a right triangle .

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a right triangle .

Ladder Leaning Against a Tree

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a…

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a right triangle .

Ladder Leaning Against a Tree

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a…

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a right triangle .

Ladder Leaning Against a Tree

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a…

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a right triangle .

Ladder Leaning Against a Tree

Illustration of a ladder leaning against a palm tree, that is perpendicular to the ground, to form a…

Illustration of 2 ladders leaning against opposite sides of a palm tree to form similar right triangles. The angles of elevation from the ground to where the ladders meet the tree are congruent. Illustration can be used for problems involving proportions.

2 Ladders Leaning Against a Tree

Illustration of 2 ladders leaning against opposite sides of a palm tree to form similar right triangles.…

Illustration of 3 ladders leaning against the side of a building (wall) to form right triangles. The distance from the base of the ladders to the wall is the same for all three ladders.

3 Ladders Leaning Against a Wall

Illustration of 3 ladders leaning against the side of a building (wall) to form right triangles. The…

Illustration of a lever with fulcrum F. W represents the weight lifted, P is the force that does the lifting, D is the distance from the fulcrum to the point of application of the force, and d is the distance from the fulcrum to the point where the weight is attached. In all possible relations of the fulcrum, weight, and force the following proportion holds: P:W = d:D.

Lever and Fulcrum

Illustration of a lever with fulcrum F. W represents the weight lifted, P is the force that does the…

An illustration of a lever with weights m and n with distances a and b from fulcrum. Illustration could be used with proportions.

Lever Balanced on fulcrum With Weights

An illustration of a lever with weights m and n with distances a and b from fulcrum. Illustration could…

Illustration of a hammer being used as a lever. F represents the fulcrum.

Hammer Used as a Lever

Illustration of a hammer being used as a lever. F represents the fulcrum.

Illustration of an ordinary steel-yard being used as a lever. F represents the fulcrum. Weight P is used to balance weight W.

Steel-yard Used as a Lever

Illustration of an ordinary steel-yard being used as a lever. F represents the fulcrum. Weight P is…

Illustration that shows if two parallel lines are cut by three or more transversals that pass through the same point, the corresponding segments are proportional.

Parallel Lines Cut by Transversals

Illustration that shows if two parallel lines are cut by three or more transversals that pass through…

Illustration that shows if two parallel lines are cut by three or more transversals that pass through the same point, the corresponding segments are proportional.

Parallel Lines Cut by Transversals

Illustration that shows if two parallel lines are cut by three or more transversals that pass through…

Illustration of two straight lines that can be used to find ratios.

Straight Lines to Find Ratios

Illustration of two straight lines that can be used to find ratios.

Illustration of 2 similar pentagons.

Similar Pentagons

Illustration of 2 similar pentagons.

Illustration of 2 similar pentagons.

Similar Pentagons

Illustration of 2 similar pentagons.

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are divided proportionally, and the section is a polygon similar to the base."

Pyramid Cut By Plane

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are…

"If two straight lines are cut by three parallel planes, the corresponding segments are proportional."

3 Parallel Planes

"If two straight lines are cut by three parallel planes, the corresponding segments are proportional."

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Similar Polygons (Pentagons) That Can Be Used To Show Proportionality

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Similar Polygons (Pentagons) That Can Be Used To Show Proportionality

Illustration that shows similar polygons (pentagons) that can be used to show proportionality.

Two similar polyhedrons may be decomposed into the same number of tetrahedrons similar, each to each, and similarly placed.

Similar Polyhedrons

Two similar polyhedrons may be decomposed into the same number of tetrahedrons similar, each to each,…

Illustration of a hydraulic machine. "A principle known as Pascal's Law states that pressure exerted on a liquid in a closed vessel is transmitted equally and undiminished in all directions." If a, A, p, and P respectively represent the areas and pressures, then the following proportion holds: a:A = p:P.

Hydraulic Machine Exerting Pressure

Illustration of a hydraulic machine. "A principle known as Pascal's Law states that pressure exerted…

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism is one half that of the larger. Hidden edges are shown.

2 Rectangular Prisms

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism…

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism is one half that of the larger.

2 Rectangular Prisms

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism…

Illustration to show that an angle bisector of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Angle Bisector of Triangle Dividing Opposite Side Into Proportionate Segments

Illustration to show that an angle bisector of a triangle divides the opposite side into segments which…

Illustration to show that a bisector of a an exterior angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Exterior Angle Bisector of Triangle Dividing Opposite Side Into Proportionate Segments

Illustration to show that a bisector of a an exterior angle of a triangle divides the opposite side…

Illustration to show that if parallel lines are cut by any number of parallels, the corresponding intercepts are proportional.

Parallel Lines Cut by Parallels, Corresponding Intercepts Proportional

Illustration to show that if parallel lines are cut by any number of parallels, the corresponding intercepts…

Illustration to show that if a line is drawn through two sides of a triangle parallel to the third side, it divides those sides proportionally.

Triangle Divided by Parallel Lines to Form Proportionate Triangles

Illustration to show that if a line is drawn through two sides of a triangle parallel to the third side,…

Illustration to show that if a line divides two sides of a triangle proportionally, it is parallel to the third side.

Triangle Divided by Parallel Lines to Form Proportionate Triangles

Illustration to show that if a line divides two sides of a triangle proportionally, it is parallel to…

Illustration used to construct a square that shall be in proportion to a given square.

Construction of Proportional Square

Illustration used to construct a square that shall be in proportion to a given square.

Illustration used to construct a square that shall be in proportion to a given square.

Construction of Proportional Square

Illustration used to construct a square that shall be in proportion to a given square.

The volumes of two similar tetrahedrons are to each other as the cubes of their homologous (corresponding) edges.

Similar Tetrahedrons

The volumes of two similar tetrahedrons are to each other as the cubes of their homologous (corresponding)…

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to each other as the products of the including edges."

Two Proportional Tetrahedrons

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to…

Illustration of a leaning tower with a perpendicular drawn from the top of the tower to the ground to form a right triangle.

Leaning Tower

Illustration of a leaning tower with a perpendicular drawn from the top of the tower to the ground to…

Illustration of a palm tree that is perpendicular to the ground. The tree is perfectly straight, as is the ground. This drawing could be used for shadow, proportion, trigonometric, or Pythagorean Theorem problems.

Palm Tree Perpendicular to Ground

Illustration of a palm tree that is perpendicular to the ground. The tree is perfectly straight, as…

Triangle diagram for measuring heights of trees using proportions.

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions.

Triangle diagram for measuring heights of trees using proportions

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions

Inclined plane using right triangle and proportions

Inclined Plane Triangle

Inclined plane using right triangle and proportions

Right triangle inscribed in semicircle. Illustration shows that the perpendicular from any point in the circumference to the diameter of a circle is the mean proportional between the segments of the diameter.

Right Triangle Inscribed in Semicircle Shows Mean Proportional

Right triangle inscribed in semicircle. Illustration shows that the perpendicular from any point in…

Illustration of oblique triangle used to find distance across a river.

Oblique Triangle for Distance Across a River

Illustration of oblique triangle used to find distance across a river.

Illustration of oblique triangle used to find distance across a river.

Oblique Triangle for Distance Across a River

Illustration of oblique triangle used to find distance across a river.

Illustration of oblique triangle used to find distance across a lake.

Oblique Triangle for Distance Across Lake

Illustration of oblique triangle used to find distance across a lake.

Similar triangles with corresponding sides labeled.

Similar Triangles

Similar triangles with corresponding sides labeled.

Similar triangles with corresponding sides labeled.

Similar Triangles

Similar triangles with corresponding sides labeled.

Illustration that shows two mutually equiangular triangles are similar.

Mutually Equiangular Similar Triangles

Illustration that shows two mutually equiangular triangles are similar.

Illustration that shows that two triangles which have their sides respectively parallel, or respectively perpendicular, are similar.

Similar Triangles With Respective Sides Parallel or Perpendicular

Illustration that shows that two triangles which have their sides respectively parallel, or respectively…